Editing Solid modeling (section)

===Cell decomposition===
This scheme follows from the combinatoric (algebraic topological) descriptions of solids detailed above. A solid can be represented by its decomposition into several cells. Spatial occupancy enumeration schemes are a particular case of cell decompositions where all the cells are cubical and lie in a regular grid. Cell decompositions provide convenient ways for computing certain [[topological properties]] of solids such as its [[Connected space|connectedness]] (number of pieces) and [[Genus (mathematics)|genus]] (number of holes). Cell decompositions in the form of triangulations are the representations used in 3D [[finite elements]] for the numerical solution of partial differential equations. Other cell decompositions such as a Whitney regular [[Topologically stratified space|stratification]] or Morse decompositions may be used for applications in robot motion planning.<ref name = "Complexity_planning">{{cite book |url=http://mitpress.mit.edu/catalog/item/default.asp?tid=4749&ttype=2 |title= The Complexity of Robot Motion Planning|author=  Canny, John F. |year= 1987 |publisher= MIT press, ACM doctoral dissertation award |access-date=20 April 2010}}</ref>